Ultimately, the work of several court architects was preferred and this artist's own preparatory work was never implemented. The agreed design itself would take hundreds of years to complete and work is still ongoing today, though more in a sense of restoration.
It was the new domed feature that would provide the biggest challenge to this ensemble of architects and other leading creative minds. This particular sketch indicates how Da Vinci was considering its form and the ways in which he would slowly experiment with different ideas.
This project is typical of the architectural contributions of the Renaissance masters, where beautiful designs were produced but ultimately never turned into reality. Whilst being considered amongst the finest draughtsmen of all time and passionate about the field of architecture, the likes of Michelangelo, Leonardo da Vinci and Raphael have very few buildings standing as examples of their work.
Da Vinci was living very close to the location of the Cathedral at the time of his work on this project and so would have been excited to potentially be contributing to the building's development. Such institutions would be embroiled in politics which would often throw up many more difficulties than when the artist was instead working within the mediums of fresco or sculpture.